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is a periodic point. That is, by a small perturbation of the original dynamical system, a system with periodic trajectory can be generated.
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to describe dissipative systems (with chaotic behavior). In the case of a dynamical system given by a map
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Pugh, Charles C. (1967). "An
Improved Closing Lemma and a General Density Theorem".
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named after him in the theory of dynamical systems. The lemma states: Let
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which is disjoint to all of the iterations of the map on it:
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https://math.berkeley.edu/people/faculty/charles-c-pugh
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127:The Closing Lemma for Dimensions Two and Three
482:{\displaystyle f^{n}(U)\cap U=\varnothing .\,}
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289:(left) with Charles Pugh, Nice, 1970
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249:{\displaystyle C^{1}}
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